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Finite Element Methods in Human Head Impact Simulations: A Review

  • Amit Madhukar
  • Martin Ostoja-StarzewskiEmail author
State-of-the-Art Modeling and Simulation of the Brain’s Response to Mechanical Loads
  • 71 Downloads

Abstract

Head impacts leading to traumatic brain injury (TBI) present a major health risk today, projected to become the third leading cause of death by 2020. While finite element (FE) models of the human brain are important tools to understand and mitigate TBI, many unresolved issues remain that need to be addressed to improve these models. This work aims to provide readers with background information regarding the current state of research in this field as well as to present recent advancements made possible by improvements to computational resources. Specifically, this has manifested as a drive to introduce more details in FE models in the form of increased spatial resolution and improved material models such as nonlinear and anisotropic constitutive models. The need to work with high-resolution FE meshes is underlined by the dominant wavelengths involved in transient pressure and shear wave propagation and the ability to model the brain surface. We also discuss improvements to experimental validation techniques which allow for better calibrated models. We review these recent developments in detail, highlighting their contributions to the field as well as identifying open issues where more research is needed.

References

  1. 1.
    Adams, J. H., D. Doyle, D. I. GRAHMA, A. E. Lawrence, D. R. McLellan, T. A. Gennarelli, M. Pastuszko, and T. Sakamoto. The contusion index: a reappraisal in human and experimental non-missile head injury. NNeuropathol. Appl. Neurobiol., 11(4):299–308, 1985.CrossRefPubMedGoogle Scholar
  2. 2.
    Al-Bsharat, A. S., W. N. Hardy, K. H. Yang, T. B. Khalil, S. Tashman, and A. I. King. Brain/skull relative displacement magnitude due to blunt head impact: new experimental data and model. Technical report, SAE Technical Paper, 1999.Google Scholar
  3. 3.
    Aldrich, E. F., H. M. Eisenberg, C. Saydjari, T. G. Luerssen, M. A. Foulkes, J. A. Jane, L. F. Marshall, A. Marmarou, and H. F. Young. Diffuse brain swelling in severely head-injured children: a report from the nih traumatic coma data bank. J. Neurosurg. 76(3):450–454, 1992.CrossRefPubMedGoogle Scholar
  4. 4.
    Alshareef, A., J. S. Giudice, J. Forman, R. S. Salzar, and M. B. Panzer. A novel method for quantifying human in situ whole brain deformation under rotational loading using sonomicrometry. J. Neurotrauma 35(5):780–789, 2018.CrossRefPubMedGoogle Scholar
  5. 5.
    Arbogast, K. B., and S. S. Margulies. Material characterization of the brainstem from oscillatory shear tests. J. Biomech. 31(9):801–807, 1998.CrossRefPubMedGoogle Scholar
  6. 6.
    Arbogast, K. B., K. L. Thibault, B. S. Pinheiro, K. I. Winey, and S. S. Margulies. A high-frequency shear device for testing soft biological tissues. J. Biomech. 30(7):757–759, 1997.CrossRefPubMedGoogle Scholar
  7. 7.
    Arfanakis, K., V. M. Haughton, J. D. Carew, B. P. Rogers, R. J. Dempsey, and M. E. Meyerand. Diffusion tensor mr imaging in diffuse axonal injury. Am. J. Neuroradiol. 23(5):794–802, 2002.PubMedGoogle Scholar
  8. 8.
    Baeck, K., J. Goffin, and J. V. Sloten. The use of different csf representations in a numerical head model and their effect on the results of fe head impact analyses. In European LS-DYNA Users Conference 2011. Proceedings 8th European LS-DYNA Users Conference, Strasbourg, France, 2011.Google Scholar
  9. 9.
    Bain, A. C., and D. F. Meaney. Tissue-level thresholds for axonal damage in an experimental model of central nervous system white matter injury. J. Biomech. Eng. 122(6):615–622, 2000.CrossRefPubMedGoogle Scholar
  10. 10.
    Bass, C. R., M. B. Panzer, K. A. Rafaels, G. Wood, J. Shridharani, and B. Capehart. Brain injuries from blast. Ann. Biomed. Eng. 40(1):185–202, 2012.CrossRefPubMedGoogle Scholar
  11. 11.
    Bazarian, J. J., J. Mcclung, M. N. Shah, Y. T. Cheng, W. Flesher, and J. Kraus. Mild traumatic brain injury in the United States, 1998–2000. Brain Inj. 19(2):85–91, 2005.CrossRefPubMedGoogle Scholar
  12. 12.
    Belytschko, T., J. Fish, and B. E. Engelmann. A finite element with embedded localization zones. Comput. Methods Appl. Mech. Eng. 70(1):59–89, 1988.CrossRefGoogle Scholar
  13. 13.
    Bilston, L. E., Z. Liu, and N. Phan-Thien. Large strain behaviour of brain tissue in shear: some experimental data and differential constitutive model. Biorheology 38(4):335–345, 2001.PubMedGoogle Scholar
  14. 14.
    Bradshaw, D. R. S., and C. L. Morfey. Pressure and shear response in brain injury models. In Proceedings of the 17th international technical conference on the enhanced safety of vehicles, Amsterdam, The Netherlands, 2001.Google Scholar
  15. 15.
    Budday, S., G. Sommer, C. Birkl, C. Langkammer, J. Haybaeck, J. Kohnert, M. Bauer, F. Paulsen, P. Steinmann, E. Kuhl, et al. Mechanical characterization of human brain tissue. Acta Biomater. 48:319–340, 2017.CrossRefPubMedGoogle Scholar
  16. 16.
    Bullock, R., and D. I. Graham. Non-penetrating injuries of the head. Cooper GJ, Dudley HAF, Gann DS et al Scientific Foundations of Trauma. Butterworth Heinemann, pp. 101–126, 1997.Google Scholar
  17. 17.
    Centers for Disease Control Prevention, et al. Report to Congress on Mild Traumatic Brain Injury in the United States: Steps to Prevent a Serious Public Health Problem. Atlanta, GA: Centers for Disease Control and Prevention, p. 45, 2003.Google Scholar
  18. 18.
    Chafi, M. S., V. Dirisala, G. Karami, and M. Ziejewski. A finite element method parametric study of the dynamic response of the human brain with different cerebrospinal fluid constitutive properties. Proc. Inst. Mech. Eng. H 223(8):1003–1019, 2009.CrossRefPubMedGoogle Scholar
  19. 19.
    Chatelin, S., A. Constantinesco, and R. Willinger. Fifty years of brain tissue mechanical testing: from in vitro to in vivo investigations. Biorheology 47(5-6):255–276, 2010.PubMedGoogle Scholar
  20. 20.
    Chatelin, S., C. Deck, F. Renard, S. Kremer, C. Heinrich, J.-P. Armspach, and R. Willinger. Computation of axonal elongation in head trauma finite element simulation. J. Mech. Behav. Biomed. Mater. 4(8):1905–1919, 2011.CrossRefPubMedGoogle Scholar
  21. 21.
    Chen, Y., and M. Ostoja-Starzewski. Mri-based finite element modeling of head trauma: spherically focusing shear waves. Acta Mech. 213(1-2):155–167, 2010.CrossRefGoogle Scholar
  22. 22.
    Chen, Y., B. Sutton, C. Conway, S. P. Broglio, and M. Ostoja-Starzewski. Brain deformation under mild impact: Magnetic resonance imaging-based assessment and finite element study. Int. J. Numer. Anal. Model. B 3(1):20–35, 2012.Google Scholar
  23. 23.
    Cheng, S., E. C. Clarke, and L. E. Bilston. Rheological properties of the tissues of the central nervous system: a review. Med. Eng. Phys. 30(10):1318–1337, 2008.CrossRefPubMedGoogle Scholar
  24. 24.
    Chu, C.-S., M.-S. Lin, H.-M. Huang, and M.-C. Lee. Finite element analysis of cerebral contusion. J. Biomech. 27(2):187–194, 1994.CrossRefPubMedGoogle Scholar
  25. 25.
    Clemmer, J., R. Prabhu, J. Chen, E. Colebeck, L. B. Priddy, M. Mccollum, B. Brazile, W. Whittington, J. L. Wardlaw, H. Rhee, et al. Experimental observation of high strain rate responses of porcine brain, liver, and tendon. J. Mech. Med. Biol., 16(03):1650032, 2016.CrossRefGoogle Scholar
  26. 26.
    Cloots, R. J. H., J. A. W. Van Dommelen, S. Kleiven, and M. G. D. Geers. Multi-scale mechanics of traumatic brain injury: predicting axonal strains from head loads. Biomech. Model. Mechanobiol. 12(1):137–150, 2013.CrossRefPubMedGoogle Scholar
  27. 27.
    Cloots, R. J. H., H. M. T. Gervaise, J. A. W. Van Dommelen, and M. G. D. Geers. Biomechanics of traumatic brain injury: influences of the morphologic heterogeneities of the cerebral cortex. Ann. Biomed.Eng. 36(7):1203, 2008.CrossRefPubMedPubMedCentralGoogle Scholar
  28. 28.
    Coats, B., S. S. Margulies, and S. Ji. Parametric study of head impact in the infant. Technical report, SAE Technical Paper, 2007.Google Scholar
  29. 29.
    Denny-Brown, D. E., and W. R. Russell. Experimental concussion:(section of neurology). Proc. R. Soc. Med. 34(11):691, 1941.PubMedPubMedCentralGoogle Scholar
  30. 30.
    Despotović, I., B. Goossens, and W. Philips. Mri segmentation of the human brain: challenges, methods, and applications. Comput. Math. Methods Med., 2015.Google Scholar
  31. 31.
    Destrade, M., B. M. Donald, J. G. Murphy, and G. Saccomandi. At least three invariants are necessary to model the mechanical response of incompressible, transversely isotropic materials. Comput. Mech. 52(4):959–969, 2013.CrossRefGoogle Scholar
  32. 32.
    Dixit, P., and G. R. Liu. A review on recent development of finite element models for head injury simulations. Arch. Comput. Methods Eng. 24(4):979–1031, 2017.CrossRefGoogle Scholar
  33. 33.
    Doblaré, M., J. M. Garcıa, and M. J. Gómez. Modelling bone tissue fracture and healing: a review. Eng. Fract. Mech. 71(13–14):1809–1840, 2004.CrossRefGoogle Scholar
  34. 34.
    Van Dommelen, J. A. W., T. P. J. Van der Sande, M. Hrapko, and G. W. M. Peters. Mechanical properties of brain tissue by indentation: interregional variation. J. Mech. Behav. Biomed. Mater. 3(2):158–166, 2010.CrossRefPubMedGoogle Scholar
  35. 35.
    Donnelly, B. R., and J. Medige. Shear properties of human brain tissue. J. Biomech. Eng. 119(4):423–432, 1997.CrossRefPubMedGoogle Scholar
  36. 36.
    Fallenstein, G. T., V. D. Hulce, and J. W. Melvin. Dynamic mechanical properties of human brain tissue. J. Biomech. 2(3):217–226, 1969.CrossRefPubMedGoogle Scholar
  37. 37.
    Famaey, N., Z. Y. Cui, G. U. Musigazi, J. Ivens, B. Depreitere, E. Verbeken, and J. Vander Sloten. Structural and mechanical characterisation of bridging veins: A review. J. Mech. Behav. Biomed. Mater. 41:222–240, 2015.CrossRefPubMedGoogle Scholar
  38. 38.
    Faul, M., M. M. Wald, L. Xu, and V. G. Coronado. Traumatic brain injury in the united states; emergency department visits, hospitalizations, and deaths, 2002–2006, 2010.Google Scholar
  39. 39.
    Feng, Y., C.-H. Lee, L. Sun, S. Ji, and X. Zhao. Characterizing white matter tissue in large strain via asymmetric indentation and inverse finite element modeling. J. Mech. Behav. Biomed. Mater. 65:490–501, 2017.CrossRefPubMedGoogle Scholar
  40. 40.
    Feng, Y., R. J. Okamoto, G. M. Genin, and P. V. Bayly. On the accuracy and fitting of transversely isotropic material models. J. Mech. Behav. Biomed. Mater. 61:554–566, 2016.CrossRefPubMedPubMedCentralGoogle Scholar
  41. 41.
    Feng, Y., R. J. Okamoto, R. Namani, G. M. Genin, and P. V. Bayly. Measurements of mechanical anisotropy in brain tissue and implications for transversely isotropic material models of white matter. J. Mech. Behav. Biomed. Mater. 23:117–132, 2013.CrossRefPubMedPubMedCentralGoogle Scholar
  42. 42.
    Fievisohn, E., Z. Bailey, A. Guettler, and P. VandeVord. Primary blast brain injury mechanisms: current knowledge, limitations, and future directions. J. Biomech. Eng. 140(2):020806, 2018.CrossRefGoogle Scholar
  43. 43.
    Finan, J. D., S. N. Sundaresh, B. S. Elkin, G. M. McKhann II, and B. Morrison III. Regional mechanical properties of human brain tissue for computational models of traumatic brain injury. Acta Biomater. 55:333–339, 2017.CrossRefPubMedGoogle Scholar
  44. 44.
    Franceschini, G., D. Bigoni, P. Regitnig, and G. A. Holzapfel. Brain tissue deforms similarly to filled elastomers and follows consolidation theory. J. Mech. Phys. Solids 54(12):2592–2620, 2006.CrossRefGoogle Scholar
  45. 45.
    Gadd, C. W. Use of a weighted-impulse criterion for estimating injury hazard. Technical report, SAE Technical Paper, 1966.Google Scholar
  46. 46.
    Ganpule, S., N. P. Daphalapurkar, K. T. Ramesh, A. K. Knutsen, D. L. Pham, P. V. Bayly, and J. L. Prince. A three-dimensional computational human head model that captures live human brain dynamics. J. Neurotrauma 34(13):2154–2166, 2017.CrossRefPubMedPubMedCentralGoogle Scholar
  47. 47.
    Garimella, H. I., and R. H. Kraft. Modeling the mechanics of axonal fiber tracts using the embedded finite element method. Int. J. Numer. Methods Biomed. Eng. 33(5):e2823, 2017.Google Scholar
  48. 48.
    Gasser, T. C., R. W. Ogden, and G. A. Holzapfel. Hyperelastic modelling of arterial layers with distributed collagen fibre orientations. J. R. Soc. Interface 3(6):15–35, 2006.CrossRefPubMedGoogle Scholar
  49. 49.
    Gefen, A., and S. S. Margulies. Are in vivo and in situ brain tissues mechanically similar? J. Biomech. 37(9):1339–1352, 2004.CrossRefPubMedGoogle Scholar
  50. 50.
    Gennarelli, T. A., L. E. Thibault, and D. I. Graham. Diffuse axonal injury: an important form of traumatic brain damage. The Neuroscientist 4(3):202–215, 1998.CrossRefGoogle Scholar
  51. 51.
    Gennarelli, T. A., L. E. Thibault, J. H. Adams, D. I. Graham, C. J. Thompson, and R. P. Marcincin. Diffuse axonal injury and traumatic coma in the primate. Ann. Neurol. 12(6):564–574, 1982.CrossRefPubMedGoogle Scholar
  52. 52.
    Gennerelli, T. A. Comparison of translational and rotational head motions in experimental cerebral concussion. In Proceedings of 15th Stapp Car Crash Conference, 1971.Google Scholar
  53. 53.
    Gentry, L.R., J. C. Godersky, and B. Thompson. MR imaging of head trauma: review of the distribution and radiopathologic features of traumatic lesions. Am. J. Roentgenol. 150(3):663–672, 1988.CrossRefGoogle Scholar
  54. 54.
    Gentry, L. R., J. C. Godersky, B. Thompson, and V. D. Dunn. Prospective comparative study of intermediate-field MR and CT in the evaluation of closed head trauma. Am. J. Roentgenol. 150(3):673–682, 1988.CrossRefGoogle Scholar
  55. 55.
    Gerber, J. I., H. T. Garimella, and R. H. Kraft. Computation of history-dependent mechanical damage of axonal fiber tracts in the brain: towards tracking sub-concussive and occupational damage to the brain. bioRxiv [Preprint], p. 346700, 2018.Google Scholar
  56. 56.
    Ghajari, M., P. J. Hellyer, and D. J. Sharp. Computational modelling of traumatic brain injury predicts the location of chronic traumatic encephalopathy pathology. Brain 140(2):333–343, 2017.CrossRefPubMedGoogle Scholar
  57. 57.
    Giordano, C., R. J. H. Cloots, J. A. W. Van Dommelen, and S. Kleiven. The influence of anisotropy on brain injury prediction. J. Biomech. 47(5):1052–1059, 2014.CrossRefPubMedGoogle Scholar
  58. 58.
    Giordano, C., and S. Kleiven. Connecting fractional anisotropy from medical images with mechanical anisotropy of a hyperviscoelastic fibre-reinforced constitutive model for brain tissue. J. R. Soc. Interface 11(91):20130914, 2014.CrossRefPubMedPubMedCentralGoogle Scholar
  59. 59.
    Giordano, C., S. Zappalà, and S. Kleiven. Anisotropic finite element models for brain injury prediction: the sensitivity of axonal strain to white matter tract inter-subject variability. Biomech. Model. Mechanobiol. 16(4):1269–1293, 2017.CrossRefPubMedPubMedCentralGoogle Scholar
  60. 60.
    Giordano, C., and S. Kleiven. Development of an unbiased validation protocol to assess the biofidelity of finite element head models used in prediction of traumatic brain injury. Technical report, SAE Technical Paper, 2016.Google Scholar
  61. 61.
    Giordano, C., and S. Kleiven. Evaluation of axonal strain as a predictor for mild traumatic brain injuries using finite element modeling. Technical report, SAE Technical Paper, 2014.Google Scholar
  62. 62.
    Graham, D. I., J. H. Adams, J. A. R. Nicoll, W. L. Maxwell, and T. A. Gennarelli. The nature, distribution and causes of traumatic brain injury. Brain Pathol. 5(4):397–406, 1995.CrossRefPubMedGoogle Scholar
  63. 63.
    Gurdjian, E. S., H. R. Lissner, J. E. Webster, F. R. Latimer, and B. F. Haddad. Studies on experimental concussion relation of physiologic effect to time duration of intracranial pressure increase at impact. Neurology 4(9):674–674, 1954.CrossRefPubMedGoogle Scholar
  64. 64.
    Hardy, W. N., C. D. Foster, M. J. Mason, K. H. Yang, A. I. King, and S. Tashman. Investigation of head injury mechanisms using neutral density technology and high-speed biplanar X-ray. Stapp Car Crash J. 45:337–368, 2001.PubMedGoogle Scholar
  65. 65.
    Hirt, C. W., A. A. Amsden, and J. L. Cook. An arbitrary lagrangian-eulerian computing method for all flow speeds. J. Comput. Phys. 14(3):227–253, 1974.CrossRefGoogle Scholar
  66. 66.
    Ho, J., and S. Kleiven. Dynamic response of the brain with vasculature: a three-dimensional computational study. J. Biomech. 40(13):3006–3012, 2007.CrossRefPubMedGoogle Scholar
  67. 67.
    Ho, J., and S. Kleiven. Can sulci protect the brain from traumatic injury? J. Biomech. 42(13):2074–2080, 2009.CrossRefPubMedGoogle Scholar
  68. 68.
    Horgan, T. J., and M. D. Gilchrist. The creation of three-dimensional finite element models for simulating head impact biomechanics. Int. J. Crashworthiness, 8(4):353–366, 2003.CrossRefGoogle Scholar
  69. 69.
    Hosey, R. R., and Y. K. Liu. A homeomorphic finite element model of the human head and neck. Finite Elem. Biomech. pp. 379–401, 1982.Google Scholar
  70. 70.
    Hrapko, M., J. A. W. Van Dommelen, G. W. M. Peters, and J. S. H. M. Wismans. The mechanical behaviour of brain tissue: large strain response and constitutive modelling. Biorheology 43(5):623–636, 2006.PubMedGoogle Scholar
  71. 71.
    Ji, S., W. Zhao, J. C. Ford, J. G. Beckwith, R. P. Bolander, R. M. Greenwald, L. A. Flashman, K. D. Paulsen, and T. W. McAllister. Group-wise evaluation and comparison of white matter fiber strain and maximum principal strain in sports-related concussion. J. Neurotrauma 32(7):441–454, 2015.CrossRefPubMedPubMedCentralGoogle Scholar
  72. 72.
    Jin, J.-X., J.-Y. Zhang, X.-W. Song, H. Hu, X.-Y. Sun, and Z.-H. Gao. Effect of cerebrospinal fluid modeled with different material properties on a human finite element head model. J. Mech. Med. Biol. 15(03):1550027, 2015.CrossRefGoogle Scholar
  73. 73.
    Jin, X., F. Zhu, H. Mao, M. Shen, and K. H. Yang. A comprehensive experimental study on material properties of human brain tissue. J. Biomech. 46(16):2795–2801, 2013.CrossRefPubMedGoogle Scholar
  74. 74.
    Johnson, K. L., S. Chowdhury, W. B. Lawrimore, Y. Mao, A. Mehmani, R. Prabhu, G. A. Rush, and M. F. Horstemeyer. Constrained topological optimization of a football helmet facemask based on brain response. Mater. Design 111:108–118, 2016.CrossRefGoogle Scholar
  75. 75.
    Johnson, C. L., M. D. J. McGarry, A. A. Gharibans, J. B. Weaver, K. D. Paulsen, H. Wang, W. C. Olivero, B. P. Sutton, and J. G. Georgiadis. Local mechanical properties of white matter structures in the human brain. Neuroimage 79:145–152, 2013.CrossRefPubMedPubMedCentralGoogle Scholar
  76. 76.
    Joldes, G. R., A. L. Lanzara, A. Wittek, B. Doyle, and K. Miller. Traumatic brain injury: an investigation into shear waves interference effects. In Computational Biomechanics for Medicine, pp. 177–186. Springer, 2016.Google Scholar
  77. 77.
    Joumaa, H., and M. Ostoja-Starzewski. Acoustic-elastodynamic interaction in isotropic fractal media. Eur. Phys. J. Special Top. 222(8):1951–1960, 2013.CrossRefGoogle Scholar
  78. 78.
    Kalmanti, E., and T. G. Maris. Fractal dimension as an index of brain cortical changes throughout life. In Vivo 21(4):641–646, 2007.PubMedGoogle Scholar
  79. 79.
    King, A. I., J. S. Ruan, C. Zhou, W. N. Hardy, and T. B. Khalil. Recent advances in biomechanics of brain injury research: a review. J. Neurotrauma 12(4):651–658, 1995.CrossRefPubMedGoogle Scholar
  80. 80.
    King, A. I., K. H. Yang, L. Zhang, W. Hardy, and D. C. Viano. Is head injury caused by linear or angular acceleration. In IRCOBI Conference, pp. 1–12. Lisbon, Portugal, 2003.Google Scholar
  81. 81.
    Kiselev, V. G., K. R. Hahn, and D. P. Auer. Is the brain cortex a fractal? Neuroimage 20(3):1765–1774, 2003.CrossRefPubMedGoogle Scholar
  82. 82.
    Kleiven, S. Evaluation of head injury criteria using a finite element model validated against experiments on localized brain motion, intracerebral acceleration, and intracranial pressure. IInt. J. Crashworthiness 11(1):65–79, 2006.CrossRefGoogle Scholar
  83. 83.
    Kleiven, S., and W. N. Hardy. Correlation of an fe model of the human head with local brain motion: Consequences for injury prediction. Stapp Car Crash J. 46:123–144, 2002.PubMedGoogle Scholar
  84. 84.
    Kleiven, S., and H. von Holst. Consequences of head size following trauma to the human head. J. Biomech. 35(2):153–160, 2002.CrossRefPubMedGoogle Scholar
  85. 85.
    Kleiven, S. Predictors for traumatic brain injuries evaluated through accident reconstructions. Technical report, SAE Technical Paper, 2007.Google Scholar
  86. 86.
    Kraft, R. H., P. J. Mckee, A. M. Dagro, and S. T. Grafton. Combining the finite element method with structural connectome-based analysis for modeling neurotrauma: connectome neurotrauma mechanics. PLoS Comput. Biol. 8(8):e1002619, 2012.CrossRefPubMedPubMedCentralGoogle Scholar
  87. 87.
    Kruse, S. A., G. H. Rose, K. J. Glaser, A. Manduca, J. P. Felmlee, C. R. Jack Jr, and R. L. Ehman. Magnetic resonance elastography of the brain. Neuroimage 39(1):231–237, 2008.CrossRefPubMedGoogle Scholar
  88. 88.
    Lindgren, S., and L. Rinder. Experimental studies in head injury. Biophysik 3(2):174–180, 1966.CrossRefPubMedGoogle Scholar
  89. 89.
    Losoi, H., N. D. Silverberg, M. Wäljas, S. Turunen, E. Rosti-Otajärvi, M. Helminen, T. M. Luoto, J. Julkunen, J. Öhman, and G. L. Iverson. Recovery from mild traumatic brain injury in previously healthy adults. J. Neurotrauma 33(8):766–776, 2016.CrossRefPubMedGoogle Scholar
  90. 90.
    MacManus, D. B., J. G. Murphy, and M. D. Gilchrist. Mechanical characterisation of brain tissue up to 35% strain at 1, 10, and 100/s using a custom-built micro-indentation apparatus. J. Mech. Behav. Biomed. Mater. 87:256–266, 2018.Google Scholar
  91. 91.
    Madhukar, A., Y. Chen, and M. Ostoja-Starzewski. Effect of cerebrospinal fluid modeling on spherically convergent shear waves during blunt head trauma. Int. J. Numer. Methods Biomed. Eng. 33(12):e2881, 2017.Google Scholar
  92. 92.
    Mao, H., H. Gao, L. Cao, V. V. Genthikatti, and K. H. Yang. Development of high-quality hexahedral human brain meshes using feature-based multi-block approach. Comput. Methods Biomech. Biomed. Eng. 16(3):271–279, 2013.CrossRefGoogle Scholar
  93. 93.
    Mao, H., L. Zhang, B. Jiang, V. V. Genthikatti, X. Jin, F. Zhu, R. Makwana, A. Gill, G. Jandir, A. Singh, et al. Development of a finite element human head model partially validated with thirty five experimental cases. J. Biomech. Eng. 135(11):111002, 2013.CrossRefPubMedGoogle Scholar
  94. 94.
    Mao, H. Modeling the head for impact scenarios. In Basic Finite Element Method as Applied to Injury Biomechanics, pp. 469–502. Elsevier, 2018.Google Scholar
  95. 95.
    Margulies, S. S., L. E. Thibault, and T. A. Gennarelli. Physical model simulations of brain injury in the primate. J. Biomech. 23(8):823–836, 1990.CrossRefPubMedGoogle Scholar
  96. 96.
    McIlwain, H., and H. S. Bachelard. Biochemistry and the central nervous system. 1972.Google Scholar
  97. 97.
    Meaney, D. F., B. Morrison, and C. D. Bass. The mechanics of traumatic brain injury: a review of what we know and what we need to know for reducing its societal burden. J. Biomech. Eng. 136(2):021008, 2014.CrossRefPubMedGoogle Scholar
  98. 98.
    Meaney, D. F., and D. H. Smith. Biomechanics of concussion. Clin. Sports Med., 30(1):19–31, 2011.CrossRefPubMedPubMedCentralGoogle Scholar
  99. 99.
    Mendis, K. K., R. L. Stalnaker, and S. H. Advani. A constitutive relationship for large deformation finite element modeling of brain tissue. J. Biomech. Eng. 117(3):279–285, 1995.CrossRefPubMedGoogle Scholar
  100. 100.
    Miller, K., and K. Chinzei. Constitutive modelling of brain tissue: experiment and theory. J. Biomech. 30(11-12):1115–1121, 1997.CrossRefPubMedGoogle Scholar
  101. 101.
    Miller, K., K. Chinzei, G. Orssengo, and P. Bednarz. Mechanical properties of brain tissue in-vivo: experiment and computer simulation. J. Biomech. 33(11):1369–1376, 2000.CrossRefPubMedGoogle Scholar
  102. 102.
    Miller, L. E., J. E. Urban, and J. D. Stitzel. Development and validation of an atlas-based finite element brain model. Biomech. Model. Mechanobiol. 15(5):1201–1214, 2016.CrossRefPubMedPubMedCentralGoogle Scholar
  103. 103.
    Miller, L. E., J. E. Urban, and J. D. Stitzel. Validation performance comparison for finite element models of the human brain. Comput. Methods Biomech. Biomed. Eng. 20(12):1273–1288, 2017.CrossRefGoogle Scholar
  104. 104.
    Morrison III, B., H. L. Cater, C. C. B. Wang, F. C. Thomas, et al. A tissue level tolerance criterion for living brain developed with an in vitro model of traumatic mechanical loading. Stapp Car Crash J. 47:93, 2003.PubMedGoogle Scholar
  105. 105.
    Nahum, A. M., R. Smith, and C. C. Ward. Intracranial pressure dynamics during head impact. Technical report, SAE Technical Paper, 1977.Google Scholar
  106. 106.
    Newman, J. A., and N. Shewchenko. A proposed new biomechanical head injury assessment function-the maximum power index. Technical report, SAE Technical Paper, 2000.Google Scholar
  107. 107.
    Ng, H. K., R. D. Mahaliyana, and W. S. Poon. The pathological spectrum of diffuse axonal injury in blunt head trauma: assessment with axon and myelin stains. Clin. Neurol. Neurosurg. 96(1):24–31, 1994.CrossRefPubMedGoogle Scholar
  108. 108.
    Nicolle, S., M. Lounis, and R. Willinger. Shear properties of brain tissue over a frequency range relevant for automotive impact situations: new experimental results. Technical report, SAE Technical Paper, 2004.Google Scholar
  109. 109.
    Ning, X., Q. Zhu, Y. Lanir, and S. S Margulies. A transversely isotropic viscoelastic constitutive equation for brainstem undergoing finite deformation. J. Biomech. Eng. 128(6):925–933, 2006.CrossRefPubMedGoogle Scholar
  110. 110.
    Ommaya, A. K. Mechanical properties of tissues of the nervous system. J. Biomech. 1(2):127–138, 1968.CrossRefPubMedGoogle Scholar
  111. 111.
    Ommaya, A. K. and T. A. Gennarelli. Cerebral concussion and traumatic unconsciousness: correlation of experimental and clinical observations on blunt head injuries. Brain 97(4):633–654, 1974.CrossRefPubMedGoogle Scholar
  112. 112.
    Ortiz, M., Y. Leroy, and A. Needleman. A finite element method for localized failure analysis. Comput. Methods Appl. Mech. Eng. 61(2):189–214, 1987.CrossRefGoogle Scholar
  113. 113.
    Peters, G. W. M., J. H. Meulman, and A. A. H. J. Sauren. The applicability of the time/temperature superposition principle to brain tissue. Biorheology 34(2):127–138, 1997.CrossRefPubMedGoogle Scholar
  114. 114.
    Post, A., and T. B. Hoshizaki. Rotational acceleration, brain tissue strain, and the relationship to concussion. J. Biomech. Eng. 137(3):030801, 2015.CrossRefGoogle Scholar
  115. 115.
    Prange, M. T. and S. S. Margulies. Regional, directional, and age-dependent properties of the brain undergoing large deformation. J. Biomech. Eng. 124(2):244–252, 2002.CrossRefPubMedGoogle Scholar
  116. 116.
    Pudenz, R. H., and C. H. Shelden. The lucite calvariuma method for direct observation of the brain: II. cranial trauma and brain movement. J. Neurosurg. 3(6):487–505, 1946.CrossRefPubMedGoogle Scholar
  117. 117.
    Qian, L., H. Zhao, Y. Guo, Y. Li, M. Zhou, L. Yang, Z. Wang, and Y. Sun. Influence of strain rate on indentation response of porcine brain. J. Mech. Behav. Biomed. Mater.J. Mech. Behav. Biomed. Mater. 82:210–217, 2018.CrossRefPubMedGoogle Scholar
  118. 118.
    Rashid, B., M. Destrade, and M. D. Gilchrist. Mechanical characterization of brain tissue in simple shear at dynamic strain rates. J. Mech. Behav. Biomed. Mater. 28:71–85, 2013.CrossRefPubMedGoogle Scholar
  119. 119.
    Rashid, B., M. Destrade, and M. D. Gilchrist. Mechanical characterization of brain tissue in tension at dynamic strain rates. J. Mech. Behav. Biomed. Mater. 33:43–54, 2014.CrossRefPubMedGoogle Scholar
  120. 120.
    de Rooij, R., and E. Kuhl. Constitutive modeling of brain tissue: current perspectives. Appl. Mech. Rev. 68(1):010801, 2016.CrossRefGoogle Scholar
  121. 121.
    Ruan, J. S., T. Khalil, and A. I. King. Human head dynamic response to side impact by finite element modeling. J. Biomech.Eng. 113(3):276–283, 1991.CrossRefPubMedGoogle Scholar
  122. 122.
    Sabet, A. A., E. Christoforou, B. Zatlin, G. M Genin, and P. V. Bayly. Deformation of the human brain induced by mild angular head acceleration. J. Biomech. 41(2):307–315, 2008.CrossRefPubMedGoogle Scholar
  123. 123.
    Sahoo, D., C. Deck, and R. Willinger. Development and validation of an advanced anisotropic visco-hyperelastic human brain fe model. J. Mech. Behav. Biomed. Mater. 33:24–42, 2014.CrossRefPubMedGoogle Scholar
  124. 124.
    Scofield, D. E., S. P. Proctor, J. R. Kardouni, O. T. Hill, and C. J. McKinnon. Risk factors for mild traumatic brain injury and subsequent post-traumatic stress disorder and mental health disorders among united states army soldiers. J. Neurotrauma 34(23):3249–3255, 2017.CrossRefGoogle Scholar
  125. 125.
    Shatsky, S. A., D. E. Evans, F. Miller, and A. N. Martins. High-speed angiography of experimental head injury. J. Neurosurg. 41(5):523–530, 1974.CrossRefPubMedGoogle Scholar
  126. 126.
    Shaw, N. A. The neurophysiology of concussion. Prog. Neurobiol. 67(4):281–344, 2002.CrossRefPubMedGoogle Scholar
  127. 127.
    Shuck, L. Z., and S. H. Advani. Rheologioal response of human brain tissue in shear. J. Fluids Eng. Trans. ASME 94(4):905–911, 1972.CrossRefGoogle Scholar
  128. 128.
    Smith, D. H., M. Nonaka, R. Miller, M. Leoni, X.-H. Chen, D. Alsop, and D. F. Meaney. Immediate coma following inertial brain injury dependent on axonal damage in the brainstem. J. Neurosurg. 93(2):315–322, 2000.CrossRefPubMedGoogle Scholar
  129. 129.
    Takhounts, E. G., R. H. Eppinger, J. Q. Campbell, R. E. Tannous, et al. On the development of the simon finite element head model. Stapp Car Crash J. 47:107, 2003.PubMedGoogle Scholar
  130. 130.
    Takhounts, E. G., S. A. Ridella, V. Hasija, R. E. Tannous, J. Q. Campbell, D. Malone, K. Danelson, J. Stitzel, S. Rowson, and S. Duma. Investigation of traumatic brain injuries using the next generation of simulated injury monitor (simon) finite element head model. Technical report, SAE Technical Paper, 2008.Google Scholar
  131. 131.
    Taylor, C. A., J. M. Bell, M. J. Breiding, and L. Xu. Traumatic brain injury-related emergency department visits, hospitalizations, and deaths-united states, 2007 and 2013. Morb. Mortal. Wkly. Rep. Surveill. Summ. 66(9):1–16, 2017.Google Scholar
  132. 132.
    Thibault, L. E., and T. A. Gennarelli. Brain injury: an analysis of neural and neurovascular trauma in the nonhuman primate. In Association for the Advancement of Automotive Medicine (AAAM), Conference, 34th, 1990, Scottsdale, Arizona, USA, 1990.Google Scholar
  133. 133.
    Toma, M., and P. D. H. Nguyen. Fluid–structure interaction analysis of cerebrospinal fluid with a comprehensive head model subject to a rapid acceleration and deceleration. Brain Inj. 32:1576–1584, 2018.Google Scholar
  134. 134.
    Tse, K. M., S. P. Lim, V. B. C. Tan, and H. P. Lee. A review of head injury and finite element head models. Am. J. Eng. Technol. Soc. 1(5):28–52, 2014.Google Scholar
  135. 135.
    Tse, K. M., L. B. Tan, S. J. Lee, S. P. Lim, and H. P. Lee. Development and validation of two subject-specific finite element models of human head against three cadaveric experiments. Int. J. Numer. Methods Biomed. Eng. 30(3):397–415, 2014.CrossRefGoogle Scholar
  136. 136.
    Velardi, F., F. Fraternali, and M. Angelillo. Anisotropic constitutive equations and experimental tensile behavior of brain tissue. Biomech. Model. Mechanobiol. 5(1):53–61, 2006.CrossRefPubMedGoogle Scholar
  137. 137.
    Versace, J. A review of the severity index. Technical report, SAE Technical Paper, 1971.Google Scholar
  138. 138.
    Viana, F. A. C., T. W. Simpson, V. Balabanov, and V. Toropov. Special section on multidisciplinary design optimization: metamodeling in multidisciplinary design optimization: how far have we really come? AIAA J. 52(4):670–690, 2014.CrossRefGoogle Scholar
  139. 139.
    Viano, D. C., I. R. Casson, E. J. Pellman, L. Zhang, A. I. King, and K. H. Yang. Concussion in professional football: brain responses by finite element analysis: part 9. Neurosurgery 57(5):891–916, 2005.CrossRefPubMedGoogle Scholar
  140. 140.
    Ward, C. C. and R. B. Thompson. The development of a detailed finite element brain model. Technical report, SAE Technical Paper, 1975.Google Scholar
  141. 141.
    Willinger, R., and D. Baumgartner. Human head tolerance limits to specific injury mechanisms. Int. J. Crashworthiness 8(6):605–617, 2003.CrossRefGoogle Scholar
  142. 142.
    Willinger, R., H.-S. Kang, and B. Diaw. Three-dimensional human head finite-element model validation against two experimental impacts. Ann. Biomed. Eng. 27(3):403–410, 1999.CrossRefPubMedGoogle Scholar
  143. 143.
    Wright, R. M., A. Post, B. Hoshizaki, and K. T. Ramesh. A multiscale computational approach to estimating axonal damage under inertial loading of the head. J. Neurotrauma 30(2):102–118, 2013.CrossRefPubMedGoogle Scholar
  144. 144.
    Yan, W., and O. D. Pangestu. A modified human head model for the study of impact head injury. Comput. Methods Biomech. Biomed. Eng. 14(12):1049–1057, 2011.CrossRefGoogle Scholar
  145. 145.
    Yang, B., K.-M. Tse, N. Chen, L.-B. Tan, Q.-Q. Zheng, H.-M. Yang, M. Hu, G. Pan, and H.-P. Lee. Development of a finite element head model for the study of impact head injury. BioMed Res. Int., 2014.Google Scholar
  146. 146.
    Yang, K. H., J. Hu, N. A. White, A. I. King, C. C. Chou, and P. Prasad. Development of numerical models for injury biomechanics research: a review of 50 years of publications in the stapp car crash conference. Technical report, SAE Technical Paper, 2006.Google Scholar
  147. 147.
    Zhang, L., K. H. Yang, R. Dwarampudi, K. Omori, T. Li, K. Chang, W. N. Hardy, T. B. Khalil, and A. I. King. Recent advances in brain injury research: a new human head model development and validation. Stapp Car Crash J. 45(11):369–394, 2001.PubMedGoogle Scholar
  148. 148.
    Zhang, L., K. H. Yang, and A. I. King. Comparison of brain responses between frontal and lateral impacts by finite element modeling. J. Neurotrauma 18(1):21–30, 2001.CrossRefPubMedGoogle Scholar
  149. 149.
    Zhang, L., K. H. Yang, and A. I. King. A proposed injury threshold for mild traumatic brain injury. J. Biomech. Eng. 126(2):226–236, 2004.CrossRefPubMedGoogle Scholar
  150. 150.
    Zhao, W., B. Choate, and S. Ji. Material properties of the brain in injury-relevant conditions—experiments and computational modeling. J. Mech. Behav. Biomed. Mater. 80:222–234, 2018.CrossRefPubMedGoogle Scholar
  151. 151.
    Zhao, W., J. C. Ford, L. A. Flashman, T. W. McAllister, and S. Ji. White matter injury susceptibility via fiber strain evaluation using whole-brain tractography. J. Neurotrauma 33(20):1834–1847, 2016.CrossRefPubMedPubMedCentralGoogle Scholar
  152. 152.
    Zhao, W., and S. Ji. Parametric investigation of regional brain strain responses via a pre-computed atlas. In IRCOBI Conference, pp. 208–220, 2015.Google Scholar
  153. 153.
    Zhou, C., T. B. Khalil, and A. I. King. A new model comparing impact responses of the homogeneous and inhomogeneous human brain. Technical report, SAE Technical Paper, 1995.Google Scholar

Copyright information

© Biomedical Engineering Society 2019

Authors and Affiliations

  1. 1.Department of Mechanical Science & EngineeringUniversity of Illinois at Urbana-ChampaignUrbanaUSA
  2. 2.Beckman Institute and Institute for Condensed Matter TheoryUniversity of Illinois at Urbana-ChampaignUrbanaUSA

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